Rewrite as a simplified fraction. ${0.90\overline{2} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 902.2222...\\ 100x &= 90.2222...\end{align*}}$ Subtracting the two equations, we have: ${900x = 812}$ ${x = \dfrac{812}{900}} $ ${x = \dfrac{203}{225}} $